The cosmic microwave background radiation defines a preferred cosmic rest
frame, and inflationary cosmological theories predict that the microwave
background temperature fluctuations should be statistically isotropic in this
rest frame. For observers moving with respect to the rest frame, the
temperature fluctuations will no longer be isotropic, due to the preferred
direction of motion. The most prominent effect is a dipole temperature
variation, which has long been observed with an amplitude of a part in a
thousand of the mean temperature. An observer's velocity with respect to the
rest frame will also induce changes in the angular correlation function and
creation of non-zero off-diagonal correlations between multipole moments. We
calculate both of these effects, which are part-in-a-thousand corrections to
the rest frame power spectrum and correlation function. Both should be
detectable in future full-sky microwave maps from the Planck satellite. These
signals will constrain cosmological models in which the cosmic dipole arises
partly from large-scale isocurvature perturbations, as suggested by recent
observations.

This paper presents a short calculation of the CMB cross-power spectrum and anisotropic correlation function created by our motion with respect to the rest frame of the CMB. The authors show that, in addition to the well-known dipole, our proper motion induces cross correlations between all multipoles and that the cross correlations between neighboring multipole values will be detectable with S/N of 5 or 6 with one channel of Planck.

They claim the interesting utility of such a detection would be in constraining non-standard cosmological models such as those with super-horizon isocurvature fluctuations that might be causing the claimed large-scale bulk flows of galaxy clusters. However, this discussion is very brief and I did not understand how such a model would be distinguished from just a different local velocity with respect to the CMB rest frame.

One issue with this is that the dipole component of the CMB lensing convergence looks exactly like angular aberration, giving the same off-diagonal correlations (which can be reconstructed using usual CMB lensing reconstruction tools). cf.

However, this discussion is very brief and I did not understand how such a model would be distinguished from just a different local velocity with respect to the CMB rest frame.

If there is a very large scale isocurvature mode, the CMB can have an intrinsic temperature dipole. Then the observed CMB dipole is the sum of the intrinsic CMB dipole and the dipole induced by our local motion.

A peculiar velocity survey can help disentangle the two as it would only show the dipole from our local motion. Peculiar velocity studies usually assume there is no large scale isocurvature mode and so take the CMB dipole to be completely due to our local motion. They then subtract off this motion from the peculiar velocity sample. They often then go on to work out the bulk flow of the sample and use this to constrain σ8. See for example, http://arxiv.org/abs/0911.5516 .

However, one can take a different perspective (see for example http://arxiv.org/abs//0711.4196 ) in which one uses the peculiar velocity survey to determine our local motion and then compares this with the estimate from the CMB dipole. If the two disagree, this could be a sign of a large scale isocurvature perturbation. The effects of the local inhomogeneity on the peculiar velocity sample can be accounted for by including the correlations they induce between peculiar velocities. So the net effect of the local inhomogeneity is to increase the error bars on the estimate of our local motion from the peculiar velocity sample.

One "disadvantage" of taken the former perspective is that if an anomalous signal is found then one has to dilute the significance by the fact that one is picking out the dipole rather than the octupole or higher moments. Whereas in the isocurvature case only the dipole of the peculiar velocity survey is important.

Joined: 13 Aug 2010Posts: 1Affiliation: University of British Columbia

Posted: August 13 2010

There's another issue which has been missed by this paper (and the newer one by Amendola at al.) - the question is precisely *which* dipole are we talking about? (imagining some extremely precise future experiment)
The solar system barycentre dipole is 369km/s towards some particular direction. But there have already been corrections made (~30km/s for the Earth's motion around the Sun, plus any motions of the satellite or experiment on the rotating Earth if you want to be precise).
A bunch of this motion is due to the Sun going round the Galaxy, plus the Galaxy falling towards Andromeda. So the "cosmic dipole" is often corrected to the Local Group frame, with a value which is actually a lot higher, currently estimated to be 627km/s (in a somewhat different direction).
Since there's no special frame, then there's no "correct" dipole to use. But presumably the aberration effect comes from the actual velocity the experiment had relative to the CMB frame when the data were taken.